# Diary of a Trainee Electronics Engineer: March 2017

**STEM, Fourier Theories & Complex Waveforms**

### STEM Soldering Workshops

In the middle of the month I ran my first STEM soldering workshop . Myself and Natasha Bissett visited a school in our local area, where we ran a soldering workshop showing a small group of four students from mixed year groups how to assemble the Cuttlefish kit.

The Cuttlefish is a PCB version of the Shrimp which is Arduino-compatible and designed for both breadboard prototyping and more permanent projects.

*Image Source: www.groundelectronics.com *

The school we visited are in the process of making a flight simulator using some rather cool motors in one of it’s STEM clubs. While there is expertise in this area from the staff, they were lacking experience amongst the students as most of them had never worked with a microcontroller platform previously. After speaking to staff from the school, it was agreed that it would be highly beneficial for the students to participate in a basic workshop which showed them how to solder and then how to run some basic Arduino sketches with the Cuttlefish board.

After speaking with the students we soon found out that some of them had soldered previously in Design Technology. The soldering workshop we ran was more of a crash course as this involved many more solder joints than they had attempted previously and some of the connections were much closer together.

Overall the students seemed to really enjoy the soldering workshop. Myself and Natasha explained what various components in the kit do and in what order we would advise soldering these into place. There were a couple of solder joints which we had to lend a helping hand with in order to get the board working, but on the whole everything went great!

In addition to showing the students how to wire up and run a blink sketch using the Arduino IDE, we also had chance to show them the AnalogReadSerial example. Here we Connected one side of a male jumper wire to pin PCO0 on the cuttlefish and then connected the other end between VCC ad GND to see what happened. This was really great as it had the kids understanding what happens when a pin is left in a floating state. We also showed them how to calculate what the voltage actually is based on the readings output in the serial monitor.

I’m really looking forward to visiting more schools in the future to run workshops similar to this. It is an incredibly rewarding feeling when you can pass on your knowledge to younger people!

### Understanding the use of complex waves

Things are gradually wrapping up on my HND course as we come closer towards the end of the year. Just as things are coming to a close we began working on one of my favourite assignments yet – understanding the use of complex waves.

When we talk about complex waves we’re usually referring to harmonics, like we are here. In electrical power systems harmonics are voltages and currents which form as a result of non-linear electric loads. Harmonics are a way of mathematically describing the distortion to a voltage or current waveform; the term ‘harmonic’ refers to a component of a waveform which occurs at an integer multiple of the fundamental frequency.

Harmonic frequencies in the power grid are a frequent cause of power quality problems and result in increased heating of equipment and conductors. The reduction of harmonics is considered desirable as this helps us to increase plant power system reliability.

#### Fourier Theories

Fourier theory states that any repetitive waveform can be defined in terms of summing sinusoidal waveforms which are integer multiples/harmonics of the fundamental frequency.

For the purposes of this assignment I had been asked to determine the Fourier series for the assigned complex waveform sample in the table.

I was then able to enter this data into a Fourier spreadsheet so that I could extract the information required to determine my waveform.

From the information in the Fourier spreadsheet I can see my harmonic values are as given:

Fundamental 200V

3rd harmonic 66.7V

5th harmonic 40V

Using this information I can determine my complex waveform, this would be:

Y=200Sinxt + 66.7Sin3xt + 40Sin5xt

Using this information I am able to then plot a graph of my complex, fundamental, 3rd & 5th harmonics using a piece of software called Autograph.

#### Calculations....

Next we calculate the impedances of each harmonic and the fundamental:

Z1 = 200 + J200

|Z1| = 282.84 A45

Z3 = 200 + J600

|Z3| = 632.45 A71.56

Z5 = 200 + J1000

|Z5| = 1019.8 A78.69

** Please note the Z values are the fundamental voltage plus the j times fundamental number multiplied by this.*

Next we can calculate the complex RMS currents. In order to do this we divide the voltage by the polar impedance of each harmonic. For example, in my case the 3rd harmonic RMS current would be:

|i3| = V3 / |Z3| = 66.7 A0 / 632.45 A71.56 = 0.105 A-71.56

Therefore the i3 RMS = 0.105 x 0.707 = 0.0742

This would be repeated for the fundamental and each harmonic like so:

|i1| = V1 / |Z1| = 200 A200 / 282.84 A45 = 0.707 A-45

i1 RMS = 0.707 x 0.707 = 0.4998

|i5| - V5 / |Z5| = 40 A0 / 1019.8 A 78.69 = 0.039 A-78.69

i5 RMS = 0.039 x 0.707 = 0.027573

Please see the image below of the current plots of the complex, fundamental, 3rd harmonic and 5th harmonic.

Next we are then able to calculate the VRMS values and the power due to each harmonic:

The RMS value of each harmonic is equal to the voltage peak of the harmonic multiplied by 0.707.

For the 3rd harmonic this would be:

V3 RMS = 66V peak x 0.707 = 46.662

Again, this would be repeated for each harmonic and the fundamental like so:

V1 RMS = 200V peak x 0.707 = 141.4

V5 RMS = 40V peak x 0.707 = 28.28

To calculate the power due to each harmonic we take the current RMS and multiply this by the voltage RMS then once again multiply this by cos of the angle of each harmonics current.

P = I RMS x V RMS x Cos(Ø)

Taking the 3rd harmonic as an example:

P3 = 0.0742 x 46.662 x cos(-71.56) = 1.1 Watts

Completing this for the fundamental and 5th harmonic we get:

P1 = 0.4998 x 141.4 x cos(-45) = 50 Watts

P5 = 0.027573 x 28.28 x cos(-78.69) = 0.15 Watts

Once this has been completed for the fundamental and each harmonic we are then able to sum these powers together to get the total power caused by harmonics, in my case this equals 51.25 watts.

I found learning to understand complex waveforms and harmonics really interesting, once again this is one of the units in my HND course which involves using a lot of formulas which I particularly enjoy.

As much as I’ve enjoyed my HND course over the past two years, it’s really nice to see things starting to wrap up as we approach the end of the year. Really looking forward to beginning my degree top-up in September now!